We developed a new method for measuring the dynamic electrophoretic mobility mu* and apparent diffusion coefficient D of colloidal particles in a sinusoidal electric field by employing the heterodyne method of light scattering. The frequency of the scattered light is sinusoidally modulated due to the Doppler effect if there is no Brownian motion of colloidal particles. The undesirable influence of Brownian motion is removed by squaring the time-domain signal, and mu* is obtained from the second and fourth harmonic components of signal detected with a lock in amplifier. On the other hand, the influence of electrophoresis is excluded to obtain D by calculating the autocorrelation function of the component at the same frequency of the applied electric field. This method is applied to a suspension of latex particles, and the complex spectrum of mu* is successfully measured for the first time in a wide frequency range below 50 kHz. The obtained spectrum of mu* shows relaxation, and the apparent diffusion coefficient D has the applied field dependence. These findings are probably due to an anomalous double-layer polarization process which has been theoretically predicted. The applicability of our method to the measurement for concentrated colloidal suspensions through which laser light cannot pass is also discussed.